I developed the following proofs to prove a beginning & end of time, I guess more from a philosophical perspective. I think they are partly related to this thread. Are there any holes in them? Have I made a mistake somewhere?
Proof of Beginning of Time
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In order to reach the present, the past must have happened, and
because an infinite amount of time cannot be passed through, the
universe must have begun a finite amount of time ago.
Proof of End of Time
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In a deterministic universe, the future in a sense has already
happened, and we can ask the question when will it end. If the future
has already happened, then the future cannot be infinitely long since
this is impossible, just as you cannot have an infinitely long piece
of string. Therefore, there is an end of time in a deterministic
universe. In a universe, where individuals have free-will, a similar
conclusion can be come to. For each free-will choice, it can be
thought that a new set of deterministic universes is 'created' and the
same as before applies for each deterministic universe.